This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A321761 #4 Nov 20 2018 19:45:53 %S A321761 1,1,1,1,0,1,1,1,1,0,1,2,1,1,1,1,1,0,0,1,0,1,0,1,2,0,1,1,2,3,1,1,1,1, %T A321761 1,1,1,0,0,0,1,3,1,1,1,1,1,1,1,1,1,1,1,0,1,1,2,2,3,4,0,0,1,2,1,3,5,0, %U A321761 0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 %N A321761 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of m(v) in s(u), where H is Heinz number, m is monomial symmetric functions, and s is Schur functions. %C A321761 Row n has length A000041(A056239(n)). %C A321761 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). %H A321761 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a> %F A321761 If s(y) = Sum_{|z| = |y|} c(y,z) * m(z), then Sum_{|z| = |y|} c(y,z) * P(z) = A296188(H(y)), where P(y) is the number of distinct permutations of y. %e A321761 Triangle begins: %e A321761 1 %e A321761 1 %e A321761 1 1 %e A321761 0 1 %e A321761 1 1 1 %e A321761 0 1 2 %e A321761 1 1 1 1 1 %e A321761 0 0 1 %e A321761 0 1 0 1 2 %e A321761 0 1 1 2 3 %e A321761 1 1 1 1 1 1 1 %e A321761 0 0 0 1 3 %e A321761 1 1 1 1 1 1 1 1 1 1 1 %e A321761 0 1 1 2 2 3 4 %e A321761 0 0 1 2 1 3 5 %e A321761 0 0 0 0 1 %e A321761 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 %e A321761 0 0 0 1 0 2 5 %e A321761 For example, row 15 gives: s(32) = m(32) + 2m(221) + m(311) + 3m(2111) + 5m(11111). %Y A321761 Row sums are A321762. %Y A321761 Cf. A000085, A008480, A056239, A082733, A124795, A153452, A296188, A300121, A321742-A321765. %K A321761 nonn,tabf %O A321761 1,12 %A A321761 _Gus Wiseman_, Nov 20 2018